Resonator circuits



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EUCH' GOTO BY United States Patent O 2,94s,s1s

RESONATOR CIRCUITS Eiichi Goto Meguro-ku, Tokyo, Japan, assigner, by mesne assignments, to Parametron Institute, Tokyo, Japan, a juridical foundation of Japan Filed May 16, 1955, Ser. No. 508,668

Claims priority, application Japan May 28, 19'54 14 Claims. (Cl. 307-88) This invention relates to improvements in and relating to non-linear circuits, and more particularly to electric resonators having reactive non-linear circuit elements and lthe application thereof to the electric computers.

For the logical elements (digital computing elements) of electric computers, the general practice has been to use electronic tubes and relays. However, the life of such tubes and relays is comparatively short, and therefore, vmuch diiiiculty is experienced in the maintenance thereof `including the replacement of such tubes and relays. Furthermore, the power consumption for the operation of such tubes and relays is fairly large, and therefore, it is necessary to supply a large amount of power by installing a large capacity plant in cases where large-sized electric computer is used. This is a great disadvantage of the device hitherto employed. Recently, transistors which consume a comparatively small amount of power were invented to replace the electronic tubes. Not only are such transistors expensive, but also the reliability and stability thereof are not yet fully known. The practical rvalue of transistors as logical elements depends largely on the future developments thereof.

The object of the present invention is to provide a resonator to be used as a logical element and as an .electrical element in general. The structure of this resonator is considerably simpler, stronger, and smallersized than that of electronic tubes and transistors. Also, this resonator is inexpensive, and can be operated perma- -nently with stability, and the power consumption thereof is very small.

The advantages of the present invention appear in the lfollowing description taken together with the accompanying drawings. It must be noted that such description is made for the purpose of exemplilication and without Alimiting the invention or the claims thereto.

In the drawings,

Figs. 1a, 1b and 1c show the connection diagrams of one embodiment of the resonator according to the present invention;

Fig. 2 is the wave form diagram showing the principle of operation of the resonator according to the present invention;

Figs. 3a, 3by and 3c are the block diagrams showing the coupling of resonators according to the present invention;

Figs. 4a and 4b are the connection diagrams showing embodiments of couplers coupling the resonators of the present invention and other circuit elements;

Fig. 5a is the circuit diagram, and Figs. 5b and 5c are the wave form diagrams, showing the principle of parametric excitation which is applied to the resonator according to the present invention;

Figs. 6a, 6b, 6c and 6d are the characteristic curves showing the experimental results of the resonator accordingto the present invention;-

Figs. 7a, 7b, 7c, 7d; 8a, 8b; 9a, and 9b are the block diagrams, and Fig. 10 is the circuit diagram, showing the "examples of circuits of computer elements in which the '2,948,818 Patented Aug. 9, 1960 resonators according to the present invention are used;

Fig. 11 is the table which shows how the arrangement of Fig. 8a behaves;

Fig. 12 shows the table of logical function which corresponds to Fig. 8a;

Fig. 13 Shows the table of logical function which corresponds to Fig. 9a; and

Figs. 14-17 show examples of circuits which perform logical operations.

Referring to the drawings, M shows a nonlinear reactor, of which the cores are, for example, laminated cores, ferrite cores, or oxide cores. The coils, L1, L1', L2 and L2 are wound as shown in the drawing. L1 and L1 are in phase and L2 and L2 are in counter phase. (L2 and L2 may be wound in the opposite direction from cores L1 and L1) L2, L2' and the capacitor C constitute a resonance circuit having the resonance frequency f. Two cores are used, and either the exciting coils L1 and L1 or the resonance coils L2 and L2 are connected in counter phase, for the purpose of maintaining a balance in order to avoid the direct coupling of the exciting current and the resonance current. To the terminals T1 and T1 of the exciting coils L1 and L1', are connected in series the exciting current source O1 having a frequency 2f, and the direct current source B which operates the cores of M at the maximum variation point of permeability y. of the magnetisation character of the cores. When switch S1 is closed and the exciting current 2f is supplied to the coils L1 and L1', the resonance circuit L2-L2-C oscillates at a frequency f (subharmonic of the order of 1/2 of the exciting frequency). Although the above resonance circuit may oscillate at a subharmonic other than 1/2 subharmonic, the oscillation most easily occurs at 1/2 subh harmonic, and therefore, the following description takes into account only for the latter case. The manner of oscillation of 1/2 subharmonic is as shown in Fig. 2. The initial oscillation of low intensity, having frequency f, existing in the resonance circuit, is built up, when the resonator is excited by a frequency 2f, by closing switch S1 at the time point in Fig. 2. Then, the amplitude rapidly increases to a certain limited intensity, at the time point and thereafter the oscillation is sustained with stability. The phase of the above oscillation cannot -be other than either one of the phases, counter to each other, shown in solid and dotted lines in Fig. 2. Once such oscillation state is established, the oscillation continues with a high stability as long as the exciting voltage is applied, and it stops when the supply of the exciting voltage is cut off by opening switch S1. However, when switch S1 is again closed and the exciting voltage with a frequency 2f is impressed, the resonance circuit oscillates again with frequency f, as described above. Whether the phase of oscillation in this case is as shown by the solid line or by the broken line in Fig. 2 depends upon the initial conditions of excitation.

The mechanism of the generation of a 1/2 subharmonic may lalso be explained as follows: Since the exciting coils L1 and L1 and the resonant coils L2 and L2 in Fig. la are wound on ferromagnetic cores in a balanced configuration, no voltage is produced in the resonant circuit L2-L2C when the exciting current only is applied. Howeve the exciting current applied to L1 and L1 causes saturation in the ferromagnetic cores, and varies the resonance frequency of the resonant circuit. Now, let us assume that a weak resonant current having a frequency f is flowing in the resonant circuit. Then, a voltage having a beat frequency between 2f for exciting current and f for the resonant current is generated in the resonant circuit. The frequency of such voltage is also f When the resonant current has a proper phase, the above beat voltage causes positive feed back which tends to increase the above resonant current, "the resonant current is rapidly increased thereby, and the self-sustained oscillation having a frequency f (1/2 subharmonic of the exciting frequency 2f) is produced in the resonant circuit. The above-mentioned positive feed back action takes place for the two oscillation phases shown by solid and broken lines in Fig. 2. Which `of the above two oscillation phases is produced depends upon the initial condition of the resonant circuit.

In order to have the above oscillation phasedetermined, the output of the phase control oscillator O2 having the frequency f is impressed, during the non-excitation period, on the resonance circuit L2-L2-C through a resistance, by making the switch S2 contact b, as shown in Fig. 1. (In the resonator according to the present invention, the electronic tube oscillator or other known oscillator may be used as a phase control oscillator.) Then, the oscillation of the frequency f impressed on the resonance circuit by O2 is amplified during the period and the oscillation state is brought about as abovementioned. Therefore, the oscillation phase in this case is definite, said phase always being determined by the relation between the phase of oscillation applied to the resonance circuit from O2 and the phase of exciting oscillation from O1. It is always possible, therefore, to take out the oscillation output of frequency f, with a definite phase, from the output terminals T2 and T2.

Similarly, when the switch S2 is made to contract a, Ithe phase angle of the voltage is shifted by 1r from that of O2, and is impressed on the resonance circuit L2-L2-C, by means of a transformer or a proper circuit which brings about the counter phase. Then, when switch S1 is closed, the oscillation having a counter phase to that of the oscillation aforementioned is produced, and the oscillation output in counter phase to that aforementioned is taken out. Assuming the phase of the aforementioned case is shown by the solid line, the phase of the present case is yas shown by the broken line in Fig. 2.

Once the oscillation is produced, the initial mode of oscillation (frequency, phase and amplitude) continues with a high stability as long as switch S1 is closed and :the exciting voltage is applied, no matter whether the output of O2 is cut 0H from the resonance circuit, whether switch S2 is switched over to a or b, or whether an alternating voltage of the frequency different from 2f is superimposed on the output of O1. This control of the phase of the oscillation wave by the phase with a low intensity of the control oscillator O2 can be compared to the operation of a thyratron where the anode voltage is interrupted and the grid voltage is varied, whereby the operating conditions are varied. (This corresponds, in the present case, to the interruption of the exciting voltage, the variation of the phase of the phase control voltage impressed on the resonance circuit, and the variation of the oscillation state.)

The above description is applicable to a case where the ferromagnetic material is used as the nonlinear element which constitutes the resonance circuit. This is also applicable to the ease of Figs. lb and 1c, where nonlinear elements D for example barium titanate capacitors C1 and C2, are connected in parallel with the condenser C or are connected in series therewith. It is possible to eliminate C. It is also possible to use both `of the coils and condensers as nonlinear reactors.

As is clear from the above description, the resonator according to the present invention can perform the amplification of the oscillation voltage and the limiting action of the oscillation amplitude, because the exciting voltage with a frequency 2f is impressed on the resonance circuit whereby the initial oscillation of low intensity and with a frequency f is rapidly amplified to a certain intensity which is continued with stability. Since the oscillation phase is either or -l-1r by the pull in phenomenon of the phase, and said oscillation phase is maintained during the excitation period, it is possible to have phase 2,948,818 i 2 1- s ,f

discrimination, and to make the memory of a signal in the form of phase, whereby the resonator according vto the present invention is suited for a logical element. Furthermore, such a resonator is constructed only with the coil L and the condenser C, and a ferromagnetic core is inserted in L for the purpose of giving nonlinear character thereto, or a ferroelectric capacitor is used as C. For this reason, the structure is `simple and inexpensive, and can be used permanently because no consumable elements are used as parts, which therefore need not be replaced. The power consumption depends upon the size of the core to be used. About 25 mw. of power was found sufficient for the oxide core with an outer diameter of 4 mm., an inner diameter of 2 mm. and a thickness l mm. If the core is smaller, the power consumption can be made smaller. The size of the resonator is smaller than electronic tubes and relays. Even in the construction of la large-sized computer which makes complicated computations, the device can be operated satisfactorily from a small power source.

When a logical operation (digital computing operation) is carried out with the known tubes and relays, the value of the logical variables (digitally represented numbers) is determined by the presence or absence of voltage or current. Therefore, a misoperation is caused by a noise which is diicult to control. When'the resonator according to the invention is used, the value of logical variables is determined by the difference of the phase of oscillation voltage (the difference by 1r), and not by the presence or absence of voltage or current. This, together with the pull in action of the phase, viniproves the S/N (signal to noise) ratio (about 70 db), and makes it possible to perform an exact logical operation without causing a misoperation due to -noise. The resonator according to the invention can also be used as an electrical element in general for other purposes than a logical computer.

Hereinafter the description is given as to the coupling where a signal is transmitted -by coupling resonators with yone another, or by coupling resonators with other elements such as `electronic tubes, transistor circuits and relay circuits.

Figs. 3a, 3b and 3c'concern the signal transmissionby coupling two resonators P1 and P2. Fig, 3a shows the impedance coupling, Fig. 3b the admittance coupling, and Fig. 3c the mutual inductance coupling. In Figs. 3, the resonators of Fig. la are shown as P1 and P2. The resonator P1, is presumed to be in the oscillation state by the exciting voltage with a frequency 2f being vapplied to the exciting terminals T1 and T1. The oscillation voltage having a frequency f of the resonance circuit P1 is impressed ou the resonance circuit P2 through the respective coupling element, namely, the coupling irnpedance Z, coupling admittance Y, or coupling coil L5. Then, where each coupling element is resistive, the phase of the voltage impressed on the resonance circuit P2 is in phase with that of the oscillation voltage of P1 .(.the frequency of the two is f). When the exciting voltage with a frequency 2f isV impressed on the exciting terminals T1 and T1' of P2, the oscillation voltage impressed on the resonance circuit P2 rapidly increases, and P2 oscillates in phase with P1 at the frequency f. Thus, the oscillation state (signal) of P1 is transmitted to P2. Then, even when the exciting voltage of P1 is cut off and the oscillation of P1 is stopped, P2 continues its oscillation, as long as the exciting voltage is impressed` on P2, and therefore, the signal of P1 is completely transferred to P2. yWhere each coupling element is reactive, adiifer'- ence of phase is produced between the oscillation Voltage of P1 and the voltage transferred to P2. In kthis case, if the phase of' exciting voltage (frequency 2f) of P1 and P2 is the same, the oscillation phase of P2 may be indefinite dueto noise. 'It is, therefore, desirable to transfer the phase off the oscillation voltage of P1 substantially in phase by making the coupling element Iresistive. The coupling elements must be designed by taking the above into consideration. For example, in case the coupling element is reactive and there is` a phase difference in the voltage transferred from P1 to P2, it is desirable to shift the phase of the exciting voltage to the extent of the phase difference. In order to reverse the phase of oscillation of P2, a transformer or other phase-inverter can be used as a coupling element.

There has been described above the case where the signal is transferred from P1 to P2. However, by reversing the order of interruption of excitation, the signal can be transferred from P2 to P1. Similarly, by successively coupling a number of resonators, the same operation can be repeated, and the signal can be transferred successivelyl The resonators can also be used with other circuit elements.

As is clear from `the above description, no direct current or voltage is` used for the input and output circuits of the resonator according to the invention. It is a circuit element operated solely by the alternating current. On the other hand, for the elements, such as tubes, transistors or relays, which have hitherto been used, direct voltage or current is used in most cases. It is` therefore necessary to use a means for converting the alternating current into the direct current, such as rectifiers, and a means for converting the direct current into alternating current, such `as modulators, in case resonators and the hitherto used elements are coupled together. Thus in order to take out the A.C. signal produced by a resonator as a D.C. signal, a phase discriminative rectifier, such as a detector for 4EM. modulation or a ring modulator for demodulation, may be used. By superimposing the A.C. voltage, the phase of which is being taken as standard, on the output voltage of a resonator, rectifying the same, and changing the polarity of the D.C. output following the phase of oscillation of a resonator, the electronic tube circuit or other circuit can be controlled and can transmit a signal. Where the D.C. signal output from an electronic tube circuit or other circuit is` to be given to a resonator, the phase discriminative modulator, such as a ring modulator or frequency doubler type magnetic (dielectric) amplier (as shown in Fig. 4), may be used. Then, the phase of the A.C. output is varied corresponding to the polarity of the D.C. signal, and said A.C. output may be used as the input signal for the resonator.

Fig. 4a shows a well-known frequency doubler type magnetic amplifier. To the primary coils Z1 and l1 of said amplifier, the A.C. current having frequency f/Z is supplied so that the cores d and d' `are saturated. In this case, if the D.C. current doesl not How in the secondary coils l2 and l2', no A.C. component appears on the secondary side. However, if the D.C. current ows from the terminals t1 and t1 to` l2 and Z2 the second harmonic of the above A.C. current having a frequency f/Z, namely the A.C. component having a frequency f, appears on the secondary side. Since the phase of such A.C. component is reversed by the polarity of the D.C. current supplied to l2 and Z2', the phase of oscillation of the resonator can be controlled by the polarity of the D.C output, by supplying the D.C. output from the tube circuit of the other circuit to the terminals t1 and t1', taking out the A.C. output having a frequency f from the terminals t2 and t2', and supplying the same to the input circuit of the resonator. It is necessary to synchro* nize the A.C. current source having a frequency f/2 and the exciting source for the resonator having a frequency 2f.

Fig. 4b also shows a form of magnetic resistance modulator. To the primary coil l1 of said modulator is supplied an A.C. current having frequency f/Z so that the core of such coil is saturated, and the D.C. current flows in the coil ld. The A.C. output having frequency f is taken out from the secondary coils l2 and l2', and in, this case, the phase of the A.C. output having a frequency f is reversed following the sense of the D.C. current in the coil ld, namely the sense of the magnetomotive force 1]/ in the core.

As the result of studies made, it has been made clear that the function of the resonator above-mentioned can be explained by the theory of parametric oscillation (I. I. Stoker: Nonlinear Vibrations, New York (1950), and N. W. McLachlan: Ordinary Nonlinear Differential Equations, London (1950)). The parametric oscillation is described hereunder with reference to Figs. 5. Fig. 5a shows the resonance circuit consisting of the coil L(t) and the capacitor C(t), where L(t) and `C(t) show thatV L and C are the functions of time t. In case L and C are.- constants, Fig. 5a is a known electric resonance circuit..

However, a certain oscillation produced in the resonance:

W-I-FGMFO, F(+ T)=F(L) (1) where, FU) is a certain periodic function having period T. (It is assumed that the resonance circuit is lossfree.)

When FU) is the sinusoidal function of time t, the Equation l is called Mathieu's differential equation:

where, u is a parameter showing out-of-tuning of the resonance circuit, and 'y is a parameter showing the intensity of excitation.

Now, it is known that the differential equation of periodic variable constant having Zw angular frequency has at least one following solution (periodic function of the second kind):

M(f)=f"t(f) (3)k where )t is constant (generally complex), and Mt) is a periodic function of time z having Zw angular frequency.

In the Equation 2, when u, fy and A are all real, it is shown that there exists an oscillatory solution in which the amplitude is built up as time elapses, as shown in Fig 5c. This oscillation is called parametric oscillation. When )t is imaginary, the oscillatory solution is that in which the amplitude modulation and the frequency modulation are effected simultaneously (Fig. 5b).

When a, 'y and are all real, the oscillation of 1/z subharmonic is the most intense.

When excitation is made by Zw angular frequency, only the oscillation of w grows up exponentially and the oscillation having other angular frequencies cannot grow up, where parameter y showing the intensity of excitation is comparatively small and the circuit loss is comparatively large. When y is considerably large and the circuit loss is very small, the oscillation, other than 1/2 subharmonic oscillation also can grow up theoretically. However, in practice, it is extremely diliicult to realize the above-mentioned requirements.

In the case of oscillation of 1/2 subharmonic, if the magnitudes of a and y are small, the approximate solution of the Equation 2 is given as follows:

emgeos 25 Pig. 5c corresponds to t-he case where B=1r/4, and the solid and broken lines show the oscillations in counterv `7 phase. The mode of building` up of said oscillations is quite the. same. This can be conrmed by the fact that, in the YEquation 3, the values of a and x are not varied but only the sign of u is reversed, when is changed to +1r. Also, the oscillation, having a phase `different by 1r/2 from that above-mentioned, is damped exponentially, as is clear from the Equation 3 in which is taken as and therefore, a remarkable pull in action of phase occurs. In such oscillation, the phase discrimination is effected.

As mentioned above, the resonator acts due to the excitation action. The exciting circuit and the resonance circuit are separately provided as in Figs. l; the oscillation. and interruption thereof are effected by the control of. the exciting circuit (such as make and break of the switch, the variation of bias voltage and the variation of frequency); the control of the oscillation frequency is effected by the frequency of the exciting source; and the determination of the oscillation phase is effected by the control of resonance circuit, namely, the phase of the voltage wave impressed on said resonance circuit during the non-excitation period. In the excitation described above in connection with Hills Equation l and Mathieus Equation 2, the amplitude grows infinitely as time elapses. However, in an actual circuit, losses exist, and either one or both of the coil L(t) and the capacitor C(t) are made nonlinear, by using a ferrite core as the core of the coil L( t), or by using a ferroelectric capacitor as C(z). Then, taking the parameter of loss as p, and by taking the parameter showing the degree of nonlineality of reactor as Mathieus Equation 2 is modified as follows:

is the term showing the loss, and u2 is the term showing nonlineality of reactor.

Judging from the above Equation 5, the amplitude is limited, and, as shown in Fig. 2, when the initial oscillation in the'state of non-excitation is excited at the time point only the 1/2 subharmonic oscillation is built up exponentially (amplifying period) which, after having reached a certain value, maintains its state with stability (steady state). It is extremely difficult to nd the exact solution of such a'nonlinear differential equation as (5). However, the Equation 5 can be solved approximately. It was confirmed theoretically and experimentally that there exist two cases, depending upon the values of a, y and p, namely:

(a) Two stable states of oscillation having the same amplitude but of counter phase. (Such a resonator having the two stable states is hereinafter referred to as a bistable resonator.) (Fig. 2 corresponds to this case (b) Three stable states consisting of the two stable states'above mentioned in (a) and a third state in which the oscillation Iis positively damped. (Such a resonator liav-ing the three stable states is hereinafter referred to as-` a tristable resonator.).

Hereunder, a description is given as to the experiments which I made on the circuit shown in Fig. la. As cores M (non-linear reactor elements), oxide cores (a kind of ferrite core) having the thickness of 2 mm., an outer diameter of 14 mm., an inner diameter of 5.5 mm., and an initial permeability of about 600 were used. On these cores, coils L1 and L1' were respectively wound with turns, and coils L2 and L2 were respectively wound'with 15 turns. The capacity of the capacitor C WaiiSOOOpf.` Resonance frequency f was about 250 kc.

To the Vterminals T1 and T1', a bias D.C. current of about 50 ma; (for operating at the most curved point of the magnetisation curve of oxide cores M), and an exciting A.C. current of about 50* ma. having a frequency 2f supplied from the exciting source O1 were applied in supeirmposition. By Varying the frequency 2f from about 300 kc. to 700` kc., the oscillation voltage (the frequency being 1/2 of that of the excitation) was measured at the terminals T2 and T2', and the load characteristics were obtained as shown in Figs. Grt-6d. In the above experiment, the output of the phase control oscillator O2 was not supplied, because such output has no relation to the load characteristics. In Fig. 6a, no load was connected; in Fig. 6b, 1 KS2 resistance was connected to T2 to T2 in parallel with the resonance circuit;` and in Figs. 6c,V and 6d, 5009 and 3009 resistances were respectively connected. With 2509, no oscillation lwas noted. It is seen that the value of oscillation voltage varies as the value of out-of-tuning varies, that there are three critical frequencies,` F1, F2 and F3, at which the value of oscillation voltage Varies suddenly, that the oscillation is Istable in the region of Fl-Fg, the above-mentioned bistable resonator region, and that the hysteresis jump, unique in the tristable resonator, occurs in the region of F2-F3. It was confirmed by the above experiment that the frequency range of oscillation becomes smaller as the load resistance decreases, and that a remarkable constant voltage characteristic exists for the resistive load. The above experiment was made with a comparatively low frequency in order to observe easily the oscillation state with a cathode ray tube. It was also found that the oscillation could be established with an oscillation frequency of up to 4 mc. (exciting frequency up to 8 Inc.), by using the same magnetic cores and about the same exciting currentr value, and by -gradually decreasing the capacity of resonance capacitor. Also, in the above experiment, it was found that the mode of oscillation (oscillation frequency, amplitude and phase) was extremely stable, even when the excitation was continued for yweeks -with a fixed exciting frequency.

From thc above description, it will be made clear that the resonator according to the invention has the amplification action, the amplitude limitation action, phase discrimination action' and memory action. Such actions, together with its simple structure, high stability, inexpensive cost, permanent life, and small consumption of power, make it possible to use the parametron not only as' an excellent logical element, but also as electrical elements in general.

Now, I shall describe the application of the resonator `in electric computers.

It is known that the electric computers, without exception, can be. constructed with the -following four circuit elements:

(a) Delay circuit,

(b) And or Or circuit, (c) Not circuit, and

(d) Branch circuit.

Fig. 7a shows an example of the delay circuit, in which the resonator circuit of" Figs. la and 1b' is represented as PA, PB, PC and such resonators are coupled together successively as shownyby coupling impedances Z. Resonators in every third place, namely PA, PD, PB, PE, and PC, PF, are taken as groups, and each group is made to oscillate or made to cease to oscillate simultaneously. Letit be assumed that only the resonators PA, PD, (group I), shown hatched, are excited, that these are' respectively in the state 0 or state 1, and that also these memorize logical variables, x, y, which take the value 0 or 1 inthe form of a particular oscillation` phase. In order to use easily logical' algebra,` the phaseof oscillation of acertain resonator'isy taken as standard, and the resonators oscillating in phase with the standard resonator are assumed to be in the state of 1 or to be memorizing 1. The resonators oscillating in counter phase are assumed to be in the state of or to be memorizing 0. It is to be noted that, diiferently Ifrom relays and tubes, the state 1 or 0 of resonator is distinguished by the phase of oscillation, and irrespective of the state 1 or 0, the amplitude of oscillation is unchanged. In this case, a part of the oscillation voltage of group I is transferred in the two senses to each resonator in the groups II and III (PB, PE, and PC, PF, adjoining the group I, through the coupling impedances Z, as shown in Fig. 3a, and each resonator in the groups II and III oscillate with a small amplitude. This lstate is shown in Fig. 7b, in which the coupling elements are not shown.

Then, when the resonators in the group II are excited, the small amplitude oscillation of the group II is amplitied through an eicient coupling, and the state of such amplified oscillation is sustained with stability in phase with the resonators of the group I. This is show-n in Fig. 7c. Then, when the excitation of the resonators of the group I is interrupted, the state becomes as shown in Fig. 7d. It is seen that Fig. 7d corresponds to Figs. 7a and 7b, but in which the state of the resonators is moved to the right by one. By repeating similar operations, the logical variables, x, y, can be shifted successively to the right, and a kind of shift registers can be obtained thereby. The above shifting of the state by alternately interrupting the excitation of the resonators of the three groups may be compared to the stepping of dekatronf By applying a logical variable x (1 or 0) to a point of such a circuit, and by repeating the above operations, x shifts successively to the right, and the delayed x can be taken out from a desired point, and therefore, such a circuit can be `used as a delay circuit.

Although the above description is made for the situation in which x shifts to` the right (I-II-IIII), such shifting can be eiiected to the left (III-II-I), by reversing the order of excitation and interruption. Resonators coupled with the oscillating resonators `are brought to the oscillation state in phase with the oscillating resonators irrespective of their coupling sense. In the above delay circuit, every third resonator was taken as a group for simultaneous excitation and the groups I, II and III were excited successively, for the purpose of `limiting the shifting sense of the logical variables to one side only.

Fig. 8a showws an example of the And circuit, in which resonators are used. Px and Py memorize respectively the logical variable, x and y, which take the value of l or 0 in the form of a particular oscillation phase, Pd is Ia constant resonator which always memorizes 0, and three such resonators are coupled with the resonator Pd respectively through the coupling element Z, with equal coupling intensity. P0 may bereplaced by a source of voltage having a definite amplitude and the phase 0. Since each oscillation voltage of PX, Py and P0 is equal, and only the phase angle thereof is either 0 or 1r, the oscillation voltage with the phase angle 1r can be represented as e, by taking the oscillation voltage with the phase angle 0, counter phase of 1r, as -e. P0 always memorizes 0. Let it be assumed that the loscillation lvoltage of P0 is -e, and the oscillation voltage of PX and Py is either e or -e, depending upon whether the variables, x and y, are l or 0. Supposing that the above oscillation voltages are applied to Pd through the coupling element Z, the coupling coei'licient being k, and that Pd is not excited, the oscillation voltage applied to Pd from PX, Py and P0 is ke, -ke or -3ke, depending 'upon whether the phase of oscillation of PX, Py and P0 is 1r or 0. In case ke and -ke exist in the three voltages vapplied to Pd, the positive and the negative voltage cancel each other, and the remaining voltage is ke or -ke, the

phase of the impressed voltage being determined thereby. Also, in case the three voltages are all -ke, the impressed voltage is -3ke. When Pd is brought to the oscillation state by excitation and amplioation to a certain amplitude e, the oscillation voltage is either e or -e, depending upon whether the small oscillating voltage impressed on Pd is ke, -ke or -3ke. This is represented in Fig. ll, and the logical function table of variables, x and y, is shown in Fig. l2. By coupling the resonator Pd with three resonators PX, Py and P0 as shown in Fig. 8a, and by always making P0 memorize 0, the oscillation phase of Pd is determined by the majority of the phase of impressed voltages. Therefore, an And circuit for the two variables, x and y, can be constructed by giving the variables, x and y, to the two resonators, IX and Py.

Similarly, an And circuit for three variables, x, y and z, can easily be constructed by adding two resonators P0 which memorize 0, besides the resonators PX, Py and PZ. Or, in case only one P0 is used, as shown in Fig. 8b, the two coupling elements Z may be added to Pd. The intensity of the impressed voltage applied to Pd from Pd through respective Z is made equal to that of the impressed voltage from PX, Py and PZ.

An Or circuit can also be constructed in the same way, namely, by replacing P0 by a resonator P1 which memorize 1, and adding the same to resonators PX and Py or PX, Py and Pz. Fig. 9a shows the Or circuit for the two variables, x and y, Fig. 13 shows the logical function table corresponding to Fig. 9a, and Fig. 9b shows the Or circuit for the three variables, x, y and z.

A Not circuit also can easily be constructed with the resonator circuits. One has only to reverse the phase in order to replace the l of the variables, x, y to 0 or vice versa, namely, by coupling the transformer T of the ratio 1:1 to the output terminals of the resonator P, and taking out from terminal t1 the output in counter phase, or by taking out the same from the counter phase Vterminal t2 of the resonator P. This is shown in Pig. l0.

Since the variable x and the inverse variable J-c' are exactly symmetric (with the same amplitude but in counter phase) in the resonator circuit, it is not necessary to provide an elaborate element for reversing the variable, such as complementing tubes, said element being neces- -sary for the logical operation circuit using electronic tubes.

Since the resonator has a large amplification action (more than 50 db amplification can easily be obtained), vit is .possible to control the oscillation state of a number of resonators by constructing a branch circuit and supplying each one of such resonators with the output of one resonator as the phase control voltage.

Thus any complicated logical operation circuits, such as arithmetic circuits (adder, subtractor, multiplier, divider, etc.) of binary, decimal or any other radix, counter circuits, arithmetic control circuits, and memory device, can be constructed with resonators according to the invention.

However, the basic logical operation of the resonators consists in determining the state of a resonator in accordance with the majority of the states of the oscillation phase of input resonators. Therefore, it occurs sometimes that a desired logical operation can be made with a simple circuit, by utilizing the above feature, without combining the aforesaid four circuit elements, when a logical operation circuit is to be constructed with resonators.

Now, I shall describe hereunder examples of other important logical operation circuits. Fig. 14 shows an example of the logical operation circuit in which resonators, x and y, representing two variables and three other resonators are connected in two stages. Fig. 15 shows the case in which resonators, x, y and z, representing three variables and another resonator are connected in one stage. Fig. 16 shows the case in which resonators, representing three variables, and three other resonators cate the constant input from P or P1 in Figs. 8 and 9,

and

signs indicate the constant input twice as intense, and the marks in the connecting lines of resonators indicate the reversal (Not) of phase. For the sake of any easy understanding, And or Or in the column C shows And or Or circuit instead of constant input. The column A shows the combination of the value of logical variables, x, y, when the phase of oscillation outf put w of the last resonator is of the value 1. The order of oscillation in each stage is supposed to progress from left to right. The logical operation circuit shown in the upper part of Fig. 15, the oscillation phase of which is determined by the majority of three inputs, can be used as a Carry element for the logical operation circuit using resonators. Such a circuit is generally used as a Carry element for the binary adder circuit. In Figs. 8a and 9a, a resonator is connected' inl one stage, to which two variables and one constant are applied. Figs. 8b and 9b correspond to Fig. 15, and a resonator is connected in one stage, to which three Variables and one constant (having twice the intensity as in the above case, Figs. 8a and 9a) are applied.

Thus the basic logical operation circuitsdescribed above above can be combined together,lor combined with other -circuits composed of tubes, relays and the like, whereby more complicated logical operation circuits may be constructed.

I claim:

1. An electric circuit for binary digital operations comprising a plurality of resonant circuits each having a resonant frequency of near f and each including an input, an output and a variable reactance the value of which is a parameter determining the resonant frequency of said resonant circuit, said resonant circuits being coupled to each other with the output of a preceding resonant circuit being coupled to the input of a succeeding resonant circuit, means for varying said parameters comprising at least two alternating power supply circuits each having a frequency 2f and a source of D.C. bias, and means applying said 2f frequency from oney of said power supply circuits to said variable reactances at least in alternate resonant circuits and applying said frequency 2f from the other of said power supply circuits to the variable reactances in the remaining resonant circuits to vary the values of said reactances and thereby generate in said resonant circuits parametric oscillations having a fre- Iquency f, said power supply circuits being coupled to said resonant circuits in balanced bucking relationship so that :said frequency 2f of the power supply circuits is not 'transmitted to said resonant circuits and the frequency f :of said resonant circuits is not transmitted back to said power supply circuits, and means for controlling each of fsaid power supply circuits for interrupting the oscillations of frequnecy f in said preceding circuit at a time just .after the parametric oscillations are generated in the succeeding resonant circuits, whereby the binary digits are :represented by the phase of the parametric oscillations :and the phase of the frequency f generated in a preceding :resonant circuit controls the phase of the frequency f generated in a subsequent resonant circuit and the oscillation generated in the subsequenty resonant circuits is maintained even after the oscillations in the preceding resonant circuit are interrupted.

2. An electric circuit ascla'imed in claim 1 in which said means for controlling each of said power supply circuits comprises means in said power supply circuits for modulating the amplitude of the frequency 2f.

.3. An electric circuit tas vclaimed in .claim 2 which said means for controlling each of said power supply circuits comprises means for interrupting the flow of current in said power supply circuits. A A

4. An electric circuit as claimed' in claim 1 in which said means for controlling each of said power supply circuits comprises means in said power supply circuits for varying the value of the D.C. bias. y D

5. An electric circuit for y binary digital, operations, comprising a resonant circuit having a resonant frequency of near f and including a variable reactance the value of which is a parameter determining the resonant frequency of said resonant circuit, means foryy varying said parameter comprising an alternating power supply circuit having a frequency 2f and a source' of D.C. biasV and means applying said 2f frequency to said variable reactance to vary the value of said reactance and .thereby generate in said resonant circuit parametric oscillations having a frequency f, said power supply circuit andv resonant circuit being decoupled from each otherso that said frequency 2f of the power supply circuit is not transmitted to said resonant circuit and the frequency f of said resonant circuit is not transmitted back to said power supply circuit, and means Afor controlling the power supply circuit for interrupting the oscillation of frequency f in said resonator circuit, whereby the binary digits are represented by the phase of the parametric oscillations and the parametric oscillations built up in said resonant circuit have only one of two possible phases which differ by which is determined by the phase of a signal impressed onsaid resonator circuit at the start of the build up of parametric oscillations therein and said oscillations continue until the means for controlling the power supply circuit is actuated even though the impressed signal is cut olf.

6. An electric circuit as claimed in claim' 5l in which said means for controlling'the power supply circuit for interrupting the oscillation of frequencylf in said reso'- nator circuit comprises means fo'r varying thevaluev of the D.C. bias. n ,y

7. Ari electric circuit as claimed in claim 5 inV which said variable reactance isa pair of non-linear magnetic iluX circuits andy said power supply is coupled thereto in balanced bucking relationship; y

8. An electric circuit as claimed iny claim 5 in which said variable reactance is a pair of nonlin'efa capacitances and said power supply circuit is coupled thereto in balanced bucking relationship. l

9. An electric circuit for binary digital operations comprising a plurality of groups of resonant circuits, each resonant circuit having a resonant frequency of near f and each including an input, an output and a variable reactance the value of which is a parameter determining the resonant frequency of saidresonant circuit, said resonant circuits being coupled toe'ach other with'the'outputs of the resonant circuits in a preceding groupbeing coupled to the inputs of resonant circuits in a succeeding group, means for varying said parameters comprising a plurality of alternating power supply circuitsone for each group and each having a frequency 2f and a sourcel of D.C. bias and means applying said 2f frequency from. each power supply circuit to said variable reactance the resonant circuits inthe respective groups of resonant circuits to vary the values of saidr'eactances andthereby generate in said resonant circuits parametric oscillations having a frequency f, said power supply circuits being coupled to said reactances inl said resonant circuits in balanced bucking relationship so that said frequencyyzfof the power supply circuits is not transmitted to said resonant circuits and the frequency f of said resonant circuits is not transmitted back to said power supply circuits, and means for controlling each of said power supply circuits for interrupting the oscillations of frequency fin theresonator circuits of a preceding group at a time justafterthe parametric oscillations are generatedlin the resonantcir- Cllits .in a succeeding group, whereby thebinary digits are represented by the phases of the parametric oscillations in the resonant circuits and the phase of the frequency f generated in a preceding resonant circuit controls the phase of the frequency f generated in a subsequent circuit, and the oscillation generated in the subsequent resonant circuit is maintained even after the oscillations in the preceding resonant circuit are interrupted.

10. An electric circuit as claimed in claim 9 in which the number of groups of resonant circuits and power supply circuits is three.

11. An electric circuit as claimed in claim 9 in which the outputs of an odd number of resonant circuits in a preceding group are coupled to the input of a single resonant circuit in a succeeding group, whereby the phase of oscillation of the single resonant circuit is controlled by the phase of the majority of input signals.

12. An electric circuit as claimed in claim 9 in which the output of a single resonant circuit in a preceding group is coupled to the inputs of `a plurality of resonant circuits in a succeeding group, whereby the phase of oscillation of the plurality of resonant circuits in the succeeding group is controlled by the phase of the single resonant circuit in the preceding group.

13. An electric circuit as claimed in claim 9 in which the output of a resonant circuit in a preceding group is coupled to the input of a resonant circuit ina succeeding group for reversing the phase of the output, whereby the phase of oscillation of the resonant circuit in a succeeding group will be opposite to the phase of the resonant circuit in the preceding group.

14. An electric circuit for binary digital operations, comprising a resonant circuit having a resonant frequency of near f and including a variable reactance the Value of which is a parameter determining the resonant frequency of said resonant circuit, means for varying said parameter comprising an alternating power supply circuit having a frequency 2f, a means for producing a D C. bias in said variable reactance, and means applying said 2f frequency to said variable reactance to vary the value of said reactance and thereby generate in said resonant circuit parametric oscillations having a frequency f, said power supply circuit and resonant circuit being -decoupled from each other so that said frequency 2f of the power supply circuit is not transmitted to said resonant circuit and the frequency f of said resonant circuit is not transmitted back to said power circuit, and means for controlling the power supply circuit for interrupting the oscillation of frequency f in said resonator circuit, whereby the binary digits are represented by the phase of the parametric oscillations and the parametric oscillations built up in said resonant circuit have only one of two possible phases which differ by which is determined by the phase of a signal impressed on said resonator circuit at the start of the build up of parametric oscillations therein, and said oscillations continue until the means for controlling the power supply circuit is actuated even though the impressed signal is cut off.

References Cited in the file of this patent UNITED STATES PATENTS 1,544,381 Elmen et a1 .lune 30, 1925 1,788,533 Marrison Jan. 13, 1931 2,697,178 Isborn Dec. 14, 1954 2,709,757 Triest May 3l, 1955 2,721,947 Isborn Oct. 25, 1955 2,770,739 Grayson et al Nov. 13, 1956 2,815,488 Von Neumann Dec. 3, 1957 2,822,480 Isborn Feb. 4, 1958 

